Symbols That Math Really Needs
Nine invented math symbols, each with a definition and example: 'equal, I hope,' a causation coefficient, a 'much greater than,' an iterated-composition operator, and a Prince-style glyph for i.
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Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2016-04-27-symbols-that-math-really-needs/ (CC BY-NC 4.0)Transcript
[1] Symbol: :≂ (wavy-equals) Meaning: equal, I hope [board: tanθ + cotθ :≂ secθ cscθ] "I mean, they should really be equal…"
[2] Symbol: —√⁚√— Meaning: yes, I know this notation is awful, but it's so ubiquitous and accepted that at this point my hands are tied [board: sin²(x) ≠ sin(sin(x))]
[3] Symbol: Inter(P) Meaning: the interesting part of set or expression P [board: P = I am a lawyer, Q = I read trees' minds, R = P∧Q, Inter(R) = Q]
[4] Symbol: r꜀ (r-sub-cause) Meaning: the causation coefficient [board: X = ice cream sales, Y = beach visits] "Intriguing… r = 0.86, but r꜀ = 0.02."
[5] Symbol: >⁚ Meaning: not just "greater," but so much greater, it isn't funny. Like, don't even joke, dude. Inequality is a real problem. [board: 10¹⁰⁰⁰ >⁚ 1000¹⁰]
[6] Symbol: a squiggly downward arrow. Meaning: and then some algebraic steps follow, which I'm fairly confident should lead to the following expression… [board: lim (x+h)ⁿ − xⁿ / h ⇝ nxⁿ⁻¹]
[7] Symbol: I (capital-I operator, k=0 to n) of fₖ(t) Meaning: fₙ∘fₙ₋₁∘…∘f₁∘f₀(t) [board: Σ, Π, I] "I knew something was missing!"
[8] Symbol: an elaborate glyph with m≠∞, w≤y, n=4, a≥b, k=2 Meaning: Looks impressive. Means nothing. "i.e., math at its finest!"
[9] Symbol: a Prince-like glyph Meaning: I defy your binary categories and petty restrictions. A: "Wait… so if i² = −1, is i positive or negative?" B: "[glyph], buddy."